LPC Xpresso has it's own and -according to opinions of users - quite functional IDE, but I think other commercial IDEs also support it (Atollic?)
STM32 Discovery boards are supposed to work with IAR, Keil and Atollic, but I had some unpleasant experiences in the pst, where on-board STLinkV2 wouldn't cooperate with neither Keil nor IAR. I finally got Keil to work by replacing some dll's with older versions, but i guess that's not the way it's supposed to work.
I think most of the commercial packages also support various FTDI-based JTAG adapters such as Turtelizer, JTAG-lock-pick (http://www.distortec.com/), Olimex stuff. I think also BusBlaster and BusPirate can be made to work like that.
LPC Xpresso is paired up with CodeRed which has it's proprietary debugger. This debugger will only work with their IDE. If you start a debug session, the debugger will be programmed (USB bootloader) and run. If you exit the IDE it will break itself.
The IDE is usable. It even contains semihosting so you don't need a FTDI cable for a debug UART. However, my first experience with LPCxpresso wasn't 'very smooth'. But it works, sort a.
Most commercial tools only run on Windows, just like most other professional PCB CAD tools.
I would go with Coocox, it's really useful. If you want to spend money on a debugger, I guess you can go with a FTDI cable. I have never tried this combination though.
I know from experience that IAR doesn't like the combination with Olimex programmers (some are FTDI cables, some are custom)> Especially the J-link clone is horrible on Windows Vista/7. I had to repower the programmer (plugging in/out USB) everytime I wanted to start a new debug session. Pretty poor.
There is also something like GDB server or something. I never got it to work flawlessly. This was both in IAR.
J-LINK EDU is also an alternative. It's only 50 euro's and supports all devices, it's fast and supports unlimited HW breakpoints. Then again, most boards contain onboard debuggers, which is sufficient for starters.
ST provides devboards with ST-Link onboard, which can be used off board as a SWD debugger for STM32 devices. The STM32 discovery boards are great value.. it breaks out all the pins (labelled), the STM32F4 even has some demo devices on it (accelero, some sound stuff), onboard debugger for <20 euro's. You are not bound to an IDE; CooCox works, just like many others.
I'm not very impressed by NXP's effort in the market. The CodeRed debugger isn't the best (ST-Link is far superior). You're bound to their toolset, which is very frustrating.